Sort a Linked List Using Merge Sort in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind merge sort when sorting a linked list?

Merge sort splits the linked list into two halves, sorts each half recursively, and then merges the two sorted halves back together.

intermediate

Why is merge sort preferred over quicksort for sorting linked lists?

Merge sort works well with linked lists because it does not require random access and can merge sorted lists efficiently by changing pointers, while quicksort needs random access which linked lists do not support efficiently.

beginner

How do you find the middle of a linked list to split it for merge sort?

Use two pointers: a slow pointer that moves one step at a time and a fast pointer that moves two steps. When the fast pointer reaches the end, the slow pointer will be at the middle.

beginner

What is the time complexity of merge sort on a linked list?

The time complexity is O(n log n), where n is the number of nodes in the linked list.

beginner

Explain how merging two sorted linked lists works in merge sort.

Compare the head nodes of both lists, pick the smaller one, and link it to the merged list. Move the pointer of the chosen list forward. Repeat until all nodes are merged.

What technique is used to find the middle of a linked list in merge sort?

A Using a stack

B Counting nodes and dividing by two

C Two pointers: slow and fast

D Random access by index

Two pointers technique uses a slow pointer moving one step and a fast pointer moving two steps to find the middle efficiently.

What is the best time complexity of merge sort on a linked list?

A O(n^2)

B O(n log n)

C O(log n)

D O(n)

Merge sort always runs in O(n log n) time for sorting linked lists.

Why is merge sort suitable for linked lists compared to quicksort?

A Quicksort uses less memory

B Merge sort uses random access

C Quicksort is faster on linked lists

D Merge sort does not require random access

Merge sort works well with linked lists because it only needs sequential access, unlike quicksort which requires random access.

What happens after splitting the linked list in merge sort?

A Sort each half recursively

B Reverse each half

C Delete one half

D Merge without sorting

After splitting, merge sort sorts each half recursively before merging.

How do you merge two sorted linked lists?

A Pick the smaller node first and link it

B Pick nodes randomly

C Concatenate lists without sorting

D Pick the larger node first

Merging involves picking the smaller node from the heads of the two lists and linking it to the merged list.

Describe the steps to sort a linked list using merge sort.

Think about dividing and conquering the list.

Explain why merge sort is efficient for linked lists compared to other sorting algorithms.

Consider how linked lists store data and how merge sort works.

Practice

1. What is the main advantage of using merge sort to sort a linked list compared to other sorting algorithms?

easy

A. Merge sort uses less memory than bubble sort for arrays.

B. Merge sort efficiently handles linked lists without random access.

C. Merge sort sorts elements in place without extra space.

D. Merge sort is the fastest sorting algorithm for small arrays.

Solution

1. Step 1: Understand linked list access

   Linked lists do not support random access, so algorithms relying on index access are inefficient.

2. Step 2: Analyze merge sort suitability

   Merge sort works by splitting and merging lists using pointers, which fits linked lists well without needing random access.

3. Final Answer:

   Merge sort efficiently handles linked lists without random access. -> Option B

4. Quick Check:

   Linked list + merge sort = efficient pointer-based sorting [OK]

Hint: Merge sort suits linked lists due to pointer-based splitting [OK]

Common Mistakes:

• Thinking merge sort sorts in place for linked lists
• Confusing merge sort speed with bubble sort
• Assuming random access is needed for merge sort

2. Which of the following is the correct way to split a linked list into two halves in JavaScript for merge sort?

easy

A. Use a for loop to iterate half the length and split at midpoint index.

B. Use array slicing to split the linked list into two arrays.

C. Use recursion to split the list by removing the head each time.

D. Use two pointers: slow moves 1 step, fast moves 2 steps until fast reaches end.

Solution

1. Step 1: Identify splitting method for linked list

   Since linked lists lack indexes, we use two pointers: slow and fast to find midpoint.

2. Step 2: Explain pointer movement

   Slow pointer moves one node at a time, fast pointer moves two nodes; when fast reaches end, slow is at midpoint.

3. Final Answer:

   Use two pointers: slow moves 1 step, fast moves 2 steps until fast reaches end. -> Option D

4. Quick Check:

   Two-pointer technique splits linked list correctly [OK]

Hint: Use slow/fast pointers to find midpoint in linked list [OK]

Common Mistakes:

• Trying to use array methods on linked lists
• Using loops with indexes on linked lists
• Splitting by removing head repeatedly

3. What will be the output linked list after applying merge sort on the list: 4 -> 2 -> 1 -> 3 -> null?

medium

A. 1 -> 2 -> 3 -> 4 -> null

B. 4 -> 3 -> 2 -> 1 -> null

C. 2 -> 1 -> 3 -> 4 -> null

D. 1 -> 3 -> 2 -> 4 -> null

Solution

1. Step 1: Split the list into halves

   Split 4->2->1->3 into 4->2 and 1->3.

2. Step 2: Recursively sort and merge halves

   Sort 4->2 to 2->4, sort 1->3 to 1->3, then merge to 1->2->3->4.

3. Final Answer:

   1 -> 2 -> 3 -> 4 -> null -> Option A

4. Quick Check:

   Sorted ascending list = 1->2->3->4 [OK]

Hint: Merge sort outputs sorted ascending linked list [OK]

Common Mistakes:

• Confusing merge order and producing descending list
• Not fully sorting sublists before merging
• Incorrectly splitting the list

4. Given this merge sort code snippet for linked lists, what is the bug?

function mergeSort(head) {
  if (!head || !head.next) return head;
  let slow = head, fast = head;
  while (fast && fast.next) {
    slow = slow.next;
    fast = fast.next.next;
  }
  let mid = slow.next;
  slow.next = null;
  let left = mergeSort(head);
  let right = mergeSort(mid);
  return merge(left, right);
}

medium

A. The mid pointer should be slow, not slow.next.

B. Slow pointer should start at head.next, not head.

C. Fast pointer should start at head.next, not head.

D. The base case should check only for head.next, not head.

Solution

1. Step 1: Analyze pointer initialization

   Fast pointer starting at head causes incorrect midpoint for even length lists.

2. Step 2: Correct mid pointer assignment

   The mid pointer should be slow, not slow.next, to correctly split the list into two halves.

3. Final Answer:

   The mid pointer should be slow, not slow.next. -> Option A

4. Quick Check:

   Mid pointer assignment = slow for correct split [OK]

Hint: Mid pointer must be slow for correct split [OK]

Common Mistakes:

• Starting fast pointer at head
• Misplacing mid pointer assignment
• Incorrect base case conditions

5. You have a linked list with nodes containing duplicate values: 3 -> 1 -> 2 -> 3 -> 2 -> null. After applying merge sort, what will be the correct sorted linked list?

hard

A. 3 -> 3 -> 2 -> 2 -> 1 -> null

B. 1 -> 2 -> 3 -> null

C. 1 -> 2 -> 2 -> 3 -> 3 -> null

D. 2 -> 1 -> 3 -> 2 -> 3 -> null

Solution

1. Step 1: Understand merge sort handles duplicates

   Merge sort compares node values and merges them in ascending order, preserving duplicates.

2. Step 2: Sort and merge duplicates

   Sorting 3->1->2->3->2 results in 1->2->2->3->3 as duplicates remain in sorted order.

3. Final Answer:

   1 -> 2 -> 2 -> 3 -> 3 -> null -> Option C

4. Quick Check:

   Duplicates sorted and preserved in ascending order [OK]

Hint: Merge sort keeps duplicates sorted in order [OK]

Common Mistakes:

• Removing duplicates by mistake
• Sorting incorrectly in descending order
• Confusing linked list with array sorting